Analysis of the loss of stability of open profile thin-walled rods, into account the imperfections of the form

Abstract

It was made the analysis of influence the geometric imperfections to form on the stability of centrally compressed thin - walled rods of open profile with different wall thickness. The software complex of finite element analysis NASTRAN was used to create computer models of rods. Shelves and walls of rods are modeled as a set of quadrangular shell elements with six degrees of freedom in the node. Geometric imperfections are modeled in the form of the first general form of loss the stability of rods with an ideal surface, which are obtained from the linear calculation of stability which is rigidly fixed at the bottom and articulated at the top. With the help of a specially created program, the amplitude of imperfections in the shape of the rods was proportional to the wall thickness. Calculations of the stability of open-profile rods were performed in a linear formulation by the Lanzosch method, and in a nonlinear formulation by the Newton-Rafson method. Was received the values of the critical load and the corresponding forms of deformation of the rods with an ideal surface and taking into account the imperfections of the shape of different amplitude. The research results of stability of open-profile rods compared to experimental, obtained in 2016 in the laboratory of the Faculty of Civil Engineering, University in Zagreb (Croatia), and analytical and numerical calculations obtained using the ABAQUS software in 2020 at the Faculty of Civil Engineering, Brest State Technical University Faculty (Belarus). Comparative analysis showed that the critical values of compressive forces obtained in this work in the calculations of the stability of the rods in a nonlinear formulation using the computational procedures of the software package NASTRAN, was less than analytical and experimental. The critical forces obtained analytically are bigger than the numerical results of all researchers. The coincidence of numerical values of critical forces was detected in the case of an open profile rod with an ideal surface thickness of 0.0011 m and a mismatch in 0.003 m. The stability of rods research, taking into account the simulated imperfections of the form showed that the increase in the amplitude of imperfections had little effect on the critical values of compressive forces. This indicates that the model of geometric imperfections of the rods in the form of a general form of loss of stability is not the most dangerous for the stability of rods with such a profile, mounting and load. Therefore, there is need in further research of stability of the rods to perform modeling of geometric imperfections, for example, as the forms of their deformation in the ultimate state and from the action of operating load, which are obtained in nonlinear formulation.